The Lennard-Jones Fluid in the Liquid-Vapour Critical Region

The equation of state of the Lennard-Jones (LJ) fluid in the liquid-vapour (LV) critical region is investigated by Molecular Dynamics simulation (MD). The calculated pressure (P ) and chemical potential (μ) are, within the simulation statistics, flat at the critical temperature between LJ reduced densities of ca. 0.26 to 0.34. The critical temperature, Tc, determined for an isotherm where (∂P/∂ρ)T = 0 and (∂μ/∂ρ)T = 0, is shown to decrease with increasing system size and pure LJ potential interaction range, rc, using a tapering function going to zero beyond rc. The value of Tc obtained by extrapolating the system size and rc to∞ is 1.316± 0.001, which is statistically within the uncertainties of previous literature values. The percolation threshold separation, rp, along the critical isotherm decreases monotonically with increasing density, ρ, and is for intermediate densities lower than that of the nearest equivalent hard-sphere system. The lines of constant percolation distance on the density-temperature projection of the phase diagram reveal a difference in qualitative behaviour, indicative of underlying structural differences on either side of the critical envelope. The mean square force in the critical region near to Tc is linear in ρ. Probability distributions of the nearest neighbour distance, absolute particle force and potential energy per molecule are presented.